As they’re sprung from prison, job-seeking New York-area ex-cons are being advised in a manual given them by parole officers to fill that questionable gap on their résumés by lying about the time they’ve done, The Post has learned.

An ex-prisoners’ manual, published by the New York Public Library under a state contract, is filled with useful tips on how to cook up whoppers to explain time spent in the big house – such as saying you freelanced, worked for a bankrupt company or were self-employed.

The self-employment fib is a “good cover-all,” says “Connections 2003 and the Job Search: A Guide for Ex-Inmates to Information Sources in New York City,” given to local ex-cons looking for work.

“You might say you typed at home, did plumbing or electrical work around the neighborhood, peddled clothing on the street or at flea markets, or tried starting your own business,” the book says.

And to hone those fabrications, the guide includes two sample résumés from made-up applicants with a criminal past “who have chosen to hide this fact in job hunting.”

One, “Peter Vasquez,” masked his four-year stint by claiming he was self-employed then worked as an assistant manager at his uncle’s food market.

Lying about one’s criminal past on an application for a federal government job is itself a federal crime punishable by up to five years in jail.

For the past decade, the pamphlet has been distributed for free by the federal probation system to any interested job seeker and city resident recently sprung from a federal lockup. It’s also given to state prisoners and to inmates at city-run Rikers Island.

Stephan Likosky, the book’s author and a library employee, sometimes passes out copies at Rikers himself, a library official said. About 10,000 copies of the book are given out yearly.

A library spokeswoman said the passages advising cons to lie “should be corrected in future editions of this book.”

One top federal official said he had no idea that the book recommends lying.

“I was not aware that this was in there. None of us has ever sat down and read the book,” said Chris Stanton, the chief U.S. probation officer for the Southern District, which covers Manhattan, The Bronx and parts of Westchester.

“We would not advocate that – absolutely not. We do the exact opposite. We tell them to be completely honest on the job application.”

Inmates at Rikers and other city-run lockups will not get any more copies of the book until the passages suggesting lying are corrected, said city Department of Correction spokesman Tom Antenen, who called that section of the book “inappropriate.”